Problem: If $a + b + c = 7$ and $x + y + z = -4$, what is $7c - 3z + 7b - 3x + 7a - 3y$ ?
Solution: $= 7a + 7b + 7c - 3x - 3y - 3z$ $= (7) \cdot (a + b + c) + (-3) \cdot (x + y + z)$ $= (7) \cdot (7) + (-3) \cdot (-4)$ $= 49 + 12$ $= 61$